The short answer is yes, as to how much magnesium helps you sleep, the long answer is a little more complicated.
Magnesium has a whole host of benefits to the human body everything from helping you sleep, through to maintaining hormone production and muscle recovery.
Whilst it’s relatively uncommon as a severe deficiency effecting less than 15% off the US population , there is a large percentage of people with minor deficiencies meaning that don’t get enough to meet they’re baseline needs, never mind benefit from any extra magnesium supplementation for sleep. And meeting these baseline needs will likely have an even greater impact on sleep quality if you’re not doing so already than someone who already gets enough magnesium.
How much magnesium per day for a man
Men need notably more magnesium per day than women with the RDI of magnesium for men being 400-420mg per day.
How much magnesium per day for a woman
Women need around 310-320mg per day to maintain healthy levels of magnesium.
Why does magnesium help you sleep?
Magnesium helps your body reduce cortisol (the stress hormone) build up allowing you to relax. Unlike other sleep supplements such as melatonin which is recommended to be taken in the hours leading up to sleep, the benefits are the same whenever you take them during the day.
As previously mentioned around 30-50% of the US population don’t get the full amount of magnesium recommended  this means that minor supplementation will help your body more effectively reduce cortisol when it’s time to rest.
Magnesium is also a GABA agonist, meaning that it is used to turn on your GABA receptors which have a sedative like effect. As this uses your own body to produce a sedative effect it’s only designed to kick in when your circadian rhythm tells you it’s time to sleep so won’t make you drowsy through the day.
Clinical Trials Showing Magnesium Helps You Sleep
Magnesium has been demonstrated to be effective in double blind placebo-controlled trials in reducing insomnia issues  when they looked at how magnesium helps you sleep, the researchers noted that 500mg seemed to be effective.
How much magnesium per day for sleep?
Whilst 500mg of magnesium per day is enough to improve sleep quality if you already have a diet which is high in magnesium it is not recommended to supplement more than 350mg per day to aid with sleep.
Sources of magnesium
The following foods  are all notably high in magnesium so if you eat a lot of these it would be best to aim for a supplement of 350mg rather than 500mg of magnesium for sleep.
- Seeds (particularly pumpkin and chia)
- Nuts (notably almonds and cashews)
- Butter (and other dairy)
Condition improvements with magnesium supplementation
It has been noted that for people with chronic fatigue syndrome, magnesium supplantation recommended, and has been shown to have benefits beyond sleep quality. 
What about other types of magnesium to help you sleep?
Magnesium doesn’t just come as one simple supplement, there are various compounds of magnesium that are commonly sold. Such as Magnesium Citrate or Magnesium Glycinate.
Does magnesium citrate help you sleep?
There is no reason that magnesium citrate should perform better than standard magnesium in terms of sleep aids, the main reason to choose magnesium citrate would be for people who have poor magnesium absorption, with most pills coming as 500mg this half and half blend would result in an intake of 250mg of magnesium.
Does magnesium glycinate help you sleep?
The amino acid glycinate is often used as a sleep aid by itself, so combining it with magnesium has increased benefits. Like magnesium citrate it also has the benefit of being easier for the body to absorb in one go. Generally speaking magnesium glycinate is the best for sleep related issues.
Does calcium magnesium and zinc help you sleep?
Calcium, magnesium and zinc pills are often combined with vitamin D, making them a great men’s health supplement overall. Whilst the bioavailability to zinc and calcium is slightly compromised when taking them together, it’s better than not having either. Zinc does also benefit sleep  with clinical deficiencies often causing insomnia. It is particularly important for men’s sleep issues as even minor deficiencies can crash hormone production leading to poor sleep. As such this may be a good magnesium supplement for men struggling with sleep.
1 – https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5786912/
2 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3703169/
3 - https://ods.od.nih.gov/factsheets/Magnesium-HealthProfessional/
4 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3201900/
5 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5713303